Problem: Solve for $x$ : $5x^2 + 30x - 80 = 0$
Solution: Dividing both sides by $5$ gives: $ x^2 + {6}x {-16} = 0 $ The coefficient on the $x$ term is $6$ and the constant term is $-16$ , so we need to find two numbers that add up to $6$ and multiply to $-16$ The two numbers $8$ and $-2$ satisfy both conditions: $ {8} + {-2} = {6} $ $ {8} \times {-2} = {-16} $ $(x + {8}) (x {-2}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 8) (x -2) = 0$ $x + 8 = 0$ or $x - 2 = 0$ Thus, $x = -8$ and $x = 2$ are the solutions.